The movement of a gene from one linkage group to another is called

The movement of a gene from one linkage group to another is called Translocation. 
Genes on the same chromosome should act as if they are linked to one another; that is, they should be part of the same linkage group.
Translocation is the movement of a  chromosomal segment to a new location in the genome. The least complex way for this event to occur is for two non-homologous chromosome arms to come close to each other so that an exchange is facilitated.
In crossing over there is exchange of a segment of chromosome between the non-sister chromatids of homologous chromosomes.